在[Optics Letters 28(2003)680]一文中引入了复分数富里哀变换,它不同于通常的两维实分数富里哀变换.在本文中我们从Wigner分布的复形的转动的观点以及从在梯度折射率介质中光的传播的观点分别阐明复分数富里哀变换的定义.新建立的量子力学纠缠态表象把复分数富里哀变换和Wigner分布联系起来.
In a recent paper of Optics Letter (Fan Hongyi and Lu Hailiang, Optics Letters 28(2003) 680) the complex fractional Fourier transform (CFFRT) is introduced, which is different from the usual two-dimensional real fractional Fourier transforms. In the present work we illuminate its definition from the point of view of rotation of the complex form of Wigner distributions as well as from the view of optical propagation mechanism in graded-index medium. The newly constructed quantum mechanical entangled state representations are used to link CFFRT to the Wigner distributions.
参考文献
| [1] | Namias V.The fractional order Fourier transform and its application to quantum mechancis [J].Inst.Math.Appl.,1980,25:241; Namias V.Fractionalization of Hankel transforms [J].Inst.Math.Appl.,1980,26:187 . |
| [2] | Namias V.The fractional order Fourier transform and its application to quantum mechancis [J].Inst.Math.Appl.,1980,25:241; Namias V.Fractionalization of Hankel transforms [J].Inst.Math.Appl.,1980,26:187 . |
| [3] | Mendlovic D,Ozakatas H M.Fractional Fourier transforms and their optical implementation:Ⅰ [J].J.Opt.Soc.Am.A,1993,10:1875. |
| [4] | Ozakatas H M,Mendlovic D.Fractional Fourier transforms and their optical implementation:Ⅱ [J].J.Opt.Soc.Am.A,10:2522 (1993); Opt.Commun.1993,101:163. |
| [5] | Ozakatas H M,Mendlovic D.Fractional Fourier transforms and their optical implementation:Ⅱ [J].J.Opt.Soc.Am.A,10:2522 (1993); Opt.Commun.1993,101:163. |
| [6] | Karasik Y B.Expression of the kernel of a fractional Fourier transform in elementary functions [J].Opt.Lett.1994,19:769. |
| [7] | Dorsch R G,Lohmann A W.Fractional Fourier transform used for a lens design problem [J].Appl.Opt.1995,34:4111. |
| [8] | Lohmann A W.Image rotation,Wigner rotation,and the fractional Fourier transforms [J].J.Opt.Soc.Am.A 1993,10:2181. |
| [9] | Mendlovic D,Ozakatas H M,Lohmann A W.Graded index fibers,Wigner-distribution functions and the fractional Fourier transforms [J].Appl.Opt.1994,33:6188. |
| [10] | Fan Hongyi,Lu Hailiang.Eigenmodes of fractional Hankel transform derived by the entangled-state method [J].Opt.Lett.,2003,28:680. |
| [11] | Erdelyi A.Higher Transcendental Functions,The Batemann Manuscript Project [M].McGraw-Hill,1953. |
| [12] | Fan Hongyi.Fractional Hankel transform studied by charge-amplitude state representations and complex fractional Fourier transform [J].Opt.Lett.,2003,28:2177; Yu L,Lu Y Y,Zeng X M,et al.Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform [J].Opt.Lett.,1998,(23)15:1158. |
| [13] | Fan Hongyi.Fractional Hankel transform studied by charge-amplitude state representations and complex fractional Fourier transform [J].Opt.Lett.,2003,28:2177; Yu L,Lu Y Y,Zeng X M,et al.Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform [J].Opt.Lett.,1998,(23)15:1158. |
| [14] | Wigner E.On the quantum correction for thermodynamic equilibrium [J].Phys.Rev.,1932,40:749. |
| [15] | Bastians M J.The Wigner distribution function applied to optical signals and system [J].Opt.Commun.,1978,25:26; Wigner distribution function and its application to first-order optics [J].J.Opt.Soc.Am.,1979,69:1710. |
| [16] | Bastians M J.The Wigner distribution function applied to optical signals and system [J].Opt.Commun.,1978,25:26; Wigner distribution function and its application to first-order optics [J].J.Opt.Soc.Am.,1979,69:1710. |
| [17] | Dirac P A M.The Principles of Quantum Mechanics [M].Oxford:Clarendon Press,1930. |
| [18] | Fan Hongyi,Klauder J R.Phys.Rev.A,1994,49:704; Fan Hongyi,Ye Xiong.Common eigenstates of two particles' center-of-mass coordinate and mass-weighted relative momentum [J].Phys.Rev.A,1995,51(4):3343;Fan Hongyi,Fan Yue.Representation of two-mode squeezing operator [J].Phys.Rev.A,1996,54:958; For a Review,see Fan Hongyi,Entangled states,squeezed states gained via the route of developing Dirac's symbolic method and their applications [J].Inter.J.Mod.Phys.,2004,18:1387-1455. |
| [19] | Fan Hongyi,Klauder J R.Phys.Rev.A,1994,49:704; Fan Hongyi,Ye Xiong.Common eigenstates of two particles' center-of-mass coordinate and mass-weighted relative momentum [J].Phys.Rev.A,1995,51(4):3343;Fan Hongyi,Fan Yue.Representation of two-mode squeezing operator [J].Phys.Rev.A,1996,54:958; For a Review,see Fan Hongyi,Entangled states,squeezed states gained via the route of developing Dirac's symbolic method and their applications [J].Inter.J.Mod.Phys.,2004,18:1387-1455. |
| [20] | Fan Hongyi,Klauder J R.Phys.Rev.A,1994,49:704; Fan Hongyi,Ye Xiong.Common eigenstates of two particles' center-of-mass coordinate and mass-weighted relative momentum [J].Phys.Rev.A,1995,51(4):3343;Fan Hongyi,Fan Yue.Representation of two-mode squeezing operator [J].Phys.Rev.A,1996,54:958; For a Review,see Fan Hongyi,Entangled states,squeezed states gained via the route of developing Dirac's symbolic method and their applications [J].Inter.J.Mod.Phys.,2004,18:1387-1455. |
| [21] | Fan Hongyi,Klauder J R.Phys.Rev.A,1994,49:704; Fan Hongyi,Ye Xiong.Common eigenstates of two particles' center-of-mass coordinate and mass-weighted relative momentum [J].Phys.Rev.A,1995,51(4):3343;Fan Hongyi,Fan Yue.Representation of two-mode squeezing operator [J].Phys.Rev.A,1996,54:958; For a Review,see Fan Hongyi,Entangled states,squeezed states gained via the route of developing Dirac's symbolic method and their applications [J].Inter.J.Mod.Phys.,2004,18:1387-1455. |
| [22] | Einstein A,Podolsky B,Rosen N.Can quantam-mechanical description of physical reality be considered complete?[J].Phys.Rev.,1935,47:777. |
| [23] | Fan Hongyi,Zaidi H R,Klauder J R.New approach for calculating the normally ordered form of squeezed operators [J].Phys.Rev.D.,1987,35:1831; For a Review,see Fan Hongyi,Operator ordering in quantum optics and the development of Dirac's symbolic method [J].Journal of Optics B:Quantum and Semiclassical Optics,2003,5:R147-R163. |
| [24] | Fan Hongyi,Zaidi H R,Klauder J R.New approach for calculating the normally ordered form of squeezed operators [J].Phys.Rev.D.,1987,35:1831; For a Review,see Fan Hongyi,Operator ordering in quantum optics and the development of Dirac's symbolic method [J].Journal of Optics B:Quantum and Semiclassical Optics,2003,5:R147-R163. |
| [25] | Wünsche A.On the IWOP technique in quantum optics [J].J.Opt.B:Quantum Semicalss.Opt.1999,1:R11. |
| [26] | Marcuse D.Light Transmission Optics [M].Van Nostrand Peinhold Company,1972. |
| [27] | Yariv A.Optical Electronics in Modern Communications [M].Oxford University Press,Inc.,1997. |
| [28] | Fan Hongyi,Xu Xuefen.Talbot effect in quadratic-index medium studied with two-variable polynomials and entangled states [J].Opt.Lett.,2004,29:1048. |
上一张
下一张
上一张
下一张
计量
- 下载量()
- 访问量()
文章评分
- 您的评分：
-
10%
-
20%
-
30%
-
40%
-
50%